By using different tools, diverse authors, Bryant in [1]}, Bor and Hernández Lamoneda in [2]}, Friedrich and Ivanov in [3]} and Niedziałomski in [4]}, have deduced integral formulas and divergence equations for Riemannian manifolds equipped with a \(\operatorname{\textsl {G}}_2\) -structure. They express the scalar curvature of the manifold in terms related with components of the intrinsic torsion of the \(\operatorname{\textsl {G}}_2\) -structure. Such terms are different in each formula. Thus it is natural to ask for the way in which all mentioned formulas are agree and the correlation between them.
